1806. Minimum Number of Operations to Reinitialize a Permutation

https://leetcode.com/problems/minimum-number-of-operations-to-reinitialize-a-permutation

Description

You are given an even integer n​​​​​​. You initially have a permutation perm of size n​​ where perm[i] == i​ **(0-indexed)**​​​​.

In one operation, you will create a new array arr, and for each i:

• If i % 2 == 0, then arr[i] = perm[i / 2].

• If i % 2 == 1, then arr[i] = perm[n / 2 + (i - 1) / 2].

You will then assign arr​​​​ to perm.

Return the minimum non-zero number of operations you need to perform on perm to return the permutation to its initial value.

Example 1:

**Input:** n = 2
**Output:** 1
**Explanation:** perm = [0,1] initially.
After the 1st operation, perm = [0,1]
So it takes only 1 operation.

Example 2:

**Input:** n = 4
**Output:** 2
**Explanation:** perm = [0,1,2,3] initially.
After the 1st operation, perm = [0,2,1,3]
After the 2nd operation, perm = [0,1,2,3]
So it takes only 2 operations.

Example 3:

**Input:** n = 6
**Output:** 4

Constraints:

• 2 <= n <= 1000

• n​​​​​​ is even.

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